Statement 1: The chord of contact of tangents from P to circle $S\equiv x^2+y^2-a^2=0$ is passing through Q. If  $l_1\&l_2$ are lengths of Tangents from P and Q to circle $S=0$ then   $PQ=\sqrt{l_1^2+l_2^2}$

Statement 2: The equation of chord of contact of tangents drawn from $P\left(x_1,y_1\right)$  to  $x^2+y^2=a^2$ is $x{x}_1+y{y}_1=a^2$

Let  $P\equiv \left(x_1,y_1\right)andQ\equiv \left(x_2,y_2\right)$

Let the equation of given circle be  $x^2+y^2=a^2$ The equation of chord of contact of tangents drawn from the $P\left(x_1,y_1\right)$  point to the given circle is  $x{x}_1+y{y}_1=a^2$

Since it passes through $Q\left(x_2,y_2\right)$

$\therefore x_1{x}_2+y_1{y}_2=a^2$

Now, $l_1=\sqrt{x_{{ }^1}^2+y_1^2-a^2},l_2=\sqrt{x_2^2+y_2^2-a^2}$

And, $PQ=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$

$=\sqrt{\left(x_1^2+y_1^2\right)+\left(x_2^2+y_2^2\right)-2a^2}\left[Using\left(1\right)\right]$

$=\sqrt{\left(x_1^2+y_1^2-a^2\right)+\left(x_2^2+y_2^2-a^2\right)}=\sqrt{l_1^2+l_2^2}$